Place the chicken and water in a Dutch oven. Bring to a boil; reduce heat. Add the onion, celery, carrots, garlic, salt, pepper, poultry seasoning and red pepper flakes. Cover and simmer for 1 hour or until chicken is tender.
Remove chicken from broth; cool. Skim fat from broth. Remove meat from bones; discard bones and skin. Cut meat into bite-size pieces; return to broth. Cover and simmer.
For spaetzle, combine the flour, salt, baking powder and nutmeg in a small bowl. Stir in the eggs, milk and parsley; blend well. With a rubber spatula, push batter through a large-hole grater or colander into simmering soup. Simmer, uncovered, for 10 minutes or until spaetzle float to the top.